Results of Hard Particle Simulations

When bounding walls exist, the particles confined within them not only collide with each other, but also collide with the walls. With the decrease of wall spacing, the frequency of particle-particle collisions will decrease, while the particle-wall collision frequency will increase. This can be demonstrated by calculation of collisions of particles in two parallel plates with the DSMC method. In Fig. 5 the result of such a simulation is shown. In the simulation [18], 2,000 representative nitrogen gas molecules with 50 cells were employed. Other parameters used here were viscosity /r= 1.656 X 10 Pa-s, molecular mass m =4.65 X 10 kg, and the ambient temperature 7 ref=273 K. Instead of the hard-sphere (HS) model, the variable hard-sphere (VHS) model was adopted in the simulation, which gives a better prediction of the viscosity-temperature dependence than the HS model. For the VHS model, the mean free path becomes ... 

The investigations show that the microfocus high speed radioscopy system is suitable for monitoring the hard particle transport during laser beam dispersing. It is possible to observe and analyse the processes inside the molten bath with the presented test equipment. As a consequence a basis for correlation with the results of a simulation is available. 

To compare molecular theoretical and molecular dynamics results, we have chosen the same wall-particle potential but have used the 6 - oo fluid particle potential. Equation 14, Instead of the truncated 6-12 LJ potential. This Is done because the molecular theory Is developed In terms of attractive particles with hard sphere cores. The parameter fi n Equation 8 Is chosen so that the density of the bulk fluid In equilibrium with the pore fluid Is the same, n a = 0.5925, as that In the MD simulations. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

In spite of the fact that the decay after excitation of the hard-potential itinerant oscillator is similar to the experimental computer simulation result of Figs. 7 and 8, we do not believe that it is the reduced model equivalent to the one-dimensional many-particle model under study. As remarked above, indeed, the e(r) function is not correctly reproduced by this reduced model. The choice of a virtual potential softer than the linear one seems also to be in line with the point of view of Balucani et al. They used an itinerant oscillator with a sinusoidal potential, which is the simplest one (to be studied via the use of CFP) to deal with the soft-potential itinerant oscillator. Note that the choice... 

Nauchitel and Pertsin have studied the melting properties of 13-, 19-, and 55-particle Lennard-Jones clusters.Questioning the validity of results obtained from free-volume simulations of such systems, they have used hard-sphere boundaries to constrain their clusters to finite volumes. The results of Nauchitel and Pertsin are most interesting for the 55-particle cluster. For certain ranges of temperature and mean density, structural evidence for surface melting was obtained projections of the cluster s coordinates, and radial density distribution functions, like those given in Fig. 17, characterize the cluster as a 13-particle icosahedral core surrounded by a fluidlike shell. However, dynamic calculations like those described for other clusters in the previous section have yet to be obtained to determine how fluidlike these outer atoms really are. 

Figure 10. Mass dependence of self-diffusion coefficient of hard-sphere test particle of mass mg in hard-sphere fluid of particles of mass m for Rg = R at density pR, = 0.9 for Rodger-Sceats friction (-----) and Smoluchowski friction (--------). 0—simulation results of Herman and Alder.

Computer simulation results for S2 are somewhat sparse and involve the usual uncertainties involved in extrapolating results for a truncated T(r) used in a periodic box to untruncated T(r) in an infinite system." Nevertheless for polarizable hard-sphere and Lennard-Jones particles, it is probably safe to say that the estimates currently available from the combined use of analytic and simulation input are enough to provide a reliable guide to the p and dependence of Sj over the full fluid range of those variables. The most comprehensive studies of have been made by Stell and Rushbrooke" and by Graben, Rushbrooke, and Stell," for the hard-sphere and Lennard-Jones cases, respectively. Both these works utilize the simulation results of Alder, Weis, and Strauss," as well as exact density-expansion results, and numerical results of the Kirkwood superposition approximation... 

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